Volume

The volume of solids is relatively less affected by pressure and temperature changes than is that of liquids or gases. For example, heating a liter of iron from 32°F (0°C) to 212°F (100°C) causes an increase in volume of less than 1%, and heating a liter of water through the same temperature range causes an increase in volume of less than 5%. But heating a liter of air from 32°F (0°C) to 212°F (100°C) causes an increase in volume of nearly 140%.

The volume of a solid object can be determined in one of two general ways, depending on whether or not a mathematical formula can be written for the object. For example, the volume of a cube can be determined if one knows the length of one side. In such a case, V = s³, or the volume of the cube is equal to the cube of the length of any one side (all sides being equal in length). The volume of a cylinder, on the other hand, is equal to the product of the area of the base multiplied by the altitude of the cylinder. For a right circular cylinder, the volume is equal to the product of the radius of the circular base (r) squared multiplied by the height (h) of the cone and by pi (π), or V = πr²h.

Many solid objects have irregular shapes for which no mathematical formula exists. One way to find the volume of such objects is to sub-divide them into recognizable shapes for which formulas do exist (such as many small cubes) and then approximate the total volume by summing the volumes of individual sub-divisions. This method of approximation can become exact by using calculus. Another way is to calculate the volume by water displacement, or the displacement of some other liquid.

Suppose, for example, that one wishes to calculate the volume of an irregularly shaped piece of rock. One way to determine that volume is first to add water to some volume-measuring instrument, such as a graduated cylinder. The exact volume of water added to the cylinder is recorded. Then, the object whose volume is to be determined is also added to the cylinder. The water in the cylinder will rise by an amount equivalent to the volume of the object. Thus, the final volume read on the cylinder less the original volume is equal to the volume of the submerged object.

This method is applicable, of course, only if the object is insoluble in water. If the object is soluble in water, then another liquid, such as alcohol or cyclohexane, can be substituted for the water.